1. Field of the Invention
The present invention relates to equalizers, and more particularly, to blind equalization of digital data in a receiver of a digital communications system.
2. Description of the Related Art
In many digital communications systems, a source generates digital information for transmission to multiple destination receivers. A transmitter processes the digital information into an encoded (e.g., error-correction encoded) and/or packetized stream of data. The stream of data is then divided into discrete blocks. Each of the blocks is mapped onto a corresponding sequence of code or symbol values (“symbols”) chosen from a pre-defined alphabet A, and generated with a period Ts, sometimes referred to as the “baud” period. Symbols may be modulated onto an analog, e.g., radio frequency (RF), carrier, in amplitude, phase, and/or frequency prior to physical transmission through the communication medium. Many methods of mapping exist and are well known in the art, and these pre-defined alphabets are generated based on certain criteria. For example, data may be mapped onto symbols of a complex data stream as pairs of in-phase (I) and quadrature phase (Q) component values that are subsequently modulated with an RF carrier.
A receiver performs several functions to demodulate and decode a received signal. Receiver functions include, for example, tuning and RF demodulation of the received signal to an intermediate frequency (IF) signal, synchronization with the RF carrier in frequency and phase, equalization, symbol detection, and decoding.
FIG. 1 shows a typical prior art communication system 100 that may be employed for transmission and reception of digital television signals. Communication system 100 comprises transmitter 101 transferring signals through transmission medium 102 to receiver 103. Transmitter 101 comprises digital encoding system 111, premodulator/pulse shaper 112, radio frequency (RF) upconverter 113, carrier oscillator 115, and transmit antenna 114. Transmitter 101 receives user data from information source 110 (such as video, audio, and/or computer files) coupled to digital encoding system 111. Digital encoding system 111 may provide analog-to-digital (A/D) conversion, error-correction encoding, and/or bit-to-symbol mapping to generate a sequence of symbols selected from a predetermined alphabet. For example, data may be mapped into a complex-valued signal stream with pairs of in-phase (I) and quadrature phase (O) components. Digital encoding system 111 provides the symbols to pre-modulator/pulse shaper 112. Pre-modulator/pulse shaper 112 modifies the symbols for the particular type of modulation, and may include a filter for pulse shaping of the symbols. The signal generated by pulse shaper 112 is provided to RF upconverter 113 which i) uses the signal to modulate a complex radio frequency (RF) carrier provided by carrier oscillator 115, and ii) amplifies and filters the signal. The modulated and amplified RF carrier is then emitted into the transmission medium 102 as an RF signal via transmit antenna 114.
Various modulation techniques, such as quadrature amplitude modulation (QAM), phase-shift keyed (PSK) modulation, or vestigial sideband (VSB) modulation are known in the art of communications to modulate the carrier. For example, modulation formats such as VSB are common formats used for transmission of digital television signals in accordance with, for example, the ATSC standard for digital television, “ATSC Digital Television Standard,” Doc. A/53B, August 2001.
For these modulation techniques, a quadrature oscillator may be employed with a complex RF upconverter in the modulator. The I signal component modulates the cosine component generated by the oscillator and the Q signal component modulates the sine component of the oscillator. VSB modulation is a form of single-sideband modulation in which the redundant sideband of a real-valued signal is removed in full by filtering, except for a small vestige of the redundant sideband. For complex VSB modulation, a complex signal is formed with the Q component being approximately the Hilbert transform of the I component. The Q-component thus contains no additional user information.
The modulated carrier signal transmitted through the medium 102 (which may be, e.g., terrestrial, cable, underwater, wire, optical fiber, atmosphere, space, etc.) comprises a series of analog pulses, each analog pulse being amplitude and/or phase modulated by a corresponding symbol in the sequence. The pulse shape used typically extends many symbol periods in time. This introduces the possibility of adjacent pulses corrupting each other, a phenomenon known as inter-symbol interference (ISI). Most propagation media introduce signal distortion, and factors that cause distortion include additive noise (static), signal strength variations (fading), phase shift variations, and multiple path delays (known as multipath). Multipath also causes ISI distortion when multiple versions of the transmitted signal, weighted and delayed differently by each path, are combined at the receiver sensor. In addition, front-end circuitry of the receiver and transmitter also introduce distortion and noise to the signal. The presence of distortion, noise, fading and multipath introduced by the overall communication channel (transmitter, receiver and propagation medium) can cause digital systems to degrade or fail completely when the bit error rate exceeds some threshold and overcomes the error tolerance of the system. Since digital systems transmit data as symbols having discrete levels of amplitude and/or phase, to the extent that a symbol is received at a level that differs from one of the allowed discrete levels, a measure of communication channel error and/or frequency response may be detected.
Returning to FIG. 1, receiver 103 includes antenna 120 receiving the signal from the medium 102, complex demodulator and sampler 121, timing recovery module 122, equalizer 123, detector 150, and carrier recovery module 124. Carrier recovery module 124 includes reference generator 126 and phase detector 125. Complex demodulator and sampler 121 translates the received signal from RF to intermediate frequency (IF), and performs complex demodulation of the received signal at IF to near baseband employing the locally generated reference for the carrier signal. Complex demodulator and sampler 121 also samples the signal based on an estimate of the symbol period. Timing recovery module 122 estimates the symbol timing period Ts, and this estimate may be fed back to complex demodulator and sampler 121 to adjust the sampling rate (e.g., via a sampling phase error). Timing recovery thus synchronizes sampling instances to the top-dead-center of the pulse shapes, and then tracks variations in the detected period and phase of Ts.
Equalizer 123 applies equalization to the received samples to suppress the effects of ISI, caused by phenomena such as i) residual timing error, ii) pulse shape/multipath distortion from the propagation channel, and/or iii) approximation of the ideal transmit and receive filters for ease of implementation. Carrier recovery module 124 generates estimates for the difference in frequency and phase (collectively referred to as angle θ) of the carrier used to modulate the symbols and the locally generated reference used for demodulation. Detector 150, typically implemented with a slicer, examines each sample to generate either a soft or hard decision for the symbol that corresponds to the sample. A slicer is a decision device that, responsive to the signal at its input, generates the projection of the nearest symbol value to the input signal from the grid of constellation points. The output of the slicer thus corresponds to one of the allowed, discrete levels. More complicated implementations of the slicer exploit channel coding and do not necessarily make nearest element decisions. Carrier recovery 124 module may use decision from detector 150 to estimate angle θ. After symbol detection, a decoder 151 reconstructs the transmitted data from the symbol sequence.
Equalizer 123 may be implemented as a filter that has the inverse characteristics of the communication channel. An estimate of the transmission characteristics of the communication channel (transfer function or impulse response) is either known or measured, and the equalization filter parameters may be set indirectly based on the estimate. The received signal is then passed through the equalizer, which compensates for the non-ideal communication channel by introducing “distortions” into the received signal which tend to cancel the distortions introduced by the communication channel.
For some digital transmission applications, such as digital television broadcasting, each receiver is in a unique location with respect to the transmitter. Accordingly, the characteristics of the communication channel are not known in advance, and may even change over time. For these applications, equalizer 123 may typically be an adaptive equalizer. An adaptive equalizer has variable filter parameters, or filter coefficients (“taps”), that are calculated by the receiver, and prior art includes many methods for adjusting the equalizer filter parameters to restore signal quality to a performance level acceptable by subsequent error-correction decoding.
In some systems including an adaptive equalizer, the parameters of the equalizer filter(s) are set using a predetermined reference signal transmitted with the data, sometimes referred to as a training sequence. The training sequence is periodically sent from the transmitter to the receiver, which compares the received and known training sequence to derive parameters of the equalizer filter(s). After several iterations (adaptively deriving the parameters over successive training sequences), the equalizer filter parameters converge to a setting that tends to compensate for the distortion characteristics of the communications channel. Periodic re-training may be employed to track variations in the channel characteristics over time.
In blind equalization, the equalizer filter parameters are derived from the received signal itself, rather than by using a training sequence. In the prior art, it is known to adjust the equalizer parameters blindly based on an error term generated with the Least Mean Squares (LMS) method. For this blind equalization, either soft or hard decisions, or best estimates, of the original input symbols, are compared with the equalizer's output signal to derive parameters of the equalizer filter(s). Blind equalization systems using the LMS algorithm in this manner with hard decisions are referred to as decision-directed (DD) systems. Other systems employ a combination of both trained and blind methods: the equalizer coefficients may be updated blindly with DD between periodic training sequence transmissions.
The DD algorithm requires a relatively “good” initial estimate of the actual values within the signal input to the receiver. However, as is the case for most communication channel conditions, a relatively poor initial estimate results in high decision error rates. Decision errors cause the successively calculated equalizer filter parameters to diverge. When the parameters diverge, they fluctuate (e.g., bounce between the maximum and minimum values), rather than converge to parameters approximating the inverse of the channel characteristics. Adaptive equalizers may use other blind cost criteria to derive parameters for the equalizer's filters.
One such blind cost criterion known in the art for adaptive equalization is the constant modulus (CM) criterion. The stochastic gradient descent of the CM criterion is known as the Constant Modulus Algorithm (CMA). The CMA algorithm is described in an article by D. N. Godard entitled “Self-Recovering Equalization in Two-Dimensional Data Communication Systems,” IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867–1875, October 1980, which is incorporated herein by reference. The CM criterion and CMA algorithm were further developed to de-couple equalization and carrier recovery functions in a receiver. Such use of the CM criterion and CMA algorithm for equalization is described in J. R. Treichler et al., “A New Approach to Multipath Correction of Constant Modulus Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 2, April 1993, which is incorporated herein by reference. Systems that make use of the CMA algorithm for adaptive equalization, are described in U.S. Pat. No. 5,872,815 to Strolle et al.
The CM criterion penalizes the deviation of i) the dispersion of the magnitude squared of the equalizer output from ii) a pre-calculated constant referred to as the “dispersion constant” or the “Godard radius.” FIGS. 2A and 2B illustrate that the CM criterion is based on deviation from a “radius” about the origin of, for example, a source constellation. FIG. 2A shows a radius 201 of an 8-PSK (phase-shift keyed) constellation plotted for real (e.g., Re or I) and imaginary (e.g., Im or Q) components. In FIG. 2A, each point (symbol) lies on the circle 204 defined by this radius 201 (termed a constant modulus system), and the CM criterion penalizes distance of a received sample (e.g., sample 202) from this circle 204. Even though the constellation may rotate, the constellation remains on the circle, and so applying a CM criterion to this constellation does not penalize spatial rotation of the constellation, for example due to residual carrier offset. FIG. 2B shows a 16-QAM constellation plotted for real and imaginary components. In FIG. 2B, groups of points (symbols) lie on corresponding concentric circles 211, 212, and 213. The CM criterion defines a radius 214 of circle 215, which is not necessarily a radius of one of the concentric circles 211, 212, and 213 (termed non-constant modulus), as a “common” radial distance from the origin for the points of the constellation. As with the constellation of FIG. 2A, the CM criterion penalizes distance of a received sample (e.g., sample 203) from this circle 215.
The CM criterion defines a cost function JCM that may be expressed as given in equation (1):JCM=E[(ρ2−|yn|2)2]  (1)where E[●] denotes the expected value operator, ρ2 is the dispersion constant (Godard radius), and yn is the equalizer output. The dispersion constant ρ2 is a quantity that can be determined from the type of modulation employed (e.g., QAM, BPSK, etc.). The dispersion constant ρ2 may be derived by calculation, by experiment, or by a combination of both for a particular implementation. The equalizer output, yn,, is a function of the received data and several parameters in the receiver chain, including timing phase, equalizer filter coefficients and carrier loop derotation angle. Hence, various combinations of these parameters may be adjusted to minimize CM cost and consequently recover the transmitted symbols.
For a single-axis modulated source such as a VSB modulated source, the CM criterion may be modified by taking the real part of yn in equation (1). The modified CM criterion is referred to as the single-axis CM (SA-CM) criterion, and is given in equation (2).JSA-CM=E[(ρ2−Re{yn}2)2]  (2)where Re {●} denotes the real-part extraction.
Given a defined cost function, the gradient of the cost function may be derived. The stochastic gradient is an approximation of the true gradient given by the instantaneous derivative of the cost function without taking the expected value. For example, the stochastic gradient of the SA-CM criterion is known as SA-CMA and is derived by taking the derivative of equation (2) with respect to the parameters of interest. Once the derivative is calculated, an error term may be defined that tends to drive the parameters to a relative minimum.
Another prior art blind equalization method employs a linear prediction (LPR) based method in conjunction with the CMA based method to adaptively set filter parameters, such as described in U.S. Pat. No. 5,909,466 to Labat et al., issued Jun. 1, 1999 (“Labat”). Blind equalization comprises two parts, and operates in the frequency domain on the input signal as follows. An LPR filter first applies amplitude equalization for the magnitude of the channel's frequency response. The LPR filter is adapted to minimize the power of its output x(n), and therefore has an output power (OP) criterionJOP=E[|X(n)|2].The LPR filter is followed by a filter with parameters adapted based on a complex-valued CM error term (e.g., generated with the CMA method) that corrects for the phase of the channel's frequency response. The LPR filter may be implemented as a finite impulse response (FIR) or more typically, as an infinite impulse response (IIR) filter via with a feedback filter.
In Labat, the combined method of blind equalization of complex signals with both LPR and CMA methods is employed during a coarse initialization mode to initialize, adapt, and converge the equalization filter parameters for modulations such as PAM, QPSK, and QAM. The combined method of blind equalization is employed from the point of initially receiving the signal (i.e., a “cold start”). Once it is determined that forward and feedback filter parameters are sufficiently close to the desired solution, the equalizer is configured to operate as a decision feedback equalizer (DFE). The DFE uses a forward FIR filter operating on the received signal combined with a feedback filter operating on past hard decisions for symbols. Blind adaptation of a DFE is typically difficult to accomplish accurately due to a phenomenon known as error propagation, where incorrect symbols that are propagated through the feedback filter path cause further symbol errors, yielding error bursts. Error bursts may cause the filter parameters to diverge. Thus, the LPR method is used to initialize the feedback filter parameters while the CMA method is used to initialize the forward filter parameters.
After the coarse initialization mode, some systems with a forward FIR filter followed by a feedback IIR filter use a hybrid architecture that switches between the DFE configuration and a linear equalizer (LE) configuration. Typically, the adaptation algorithm and equalizer structure modes should then smoothly transition from acquisition mode, where the CMA method is used to adapt the LE filter parameters, to tracking mode, where a DD method is used to update the DFE filter parameters. Such hybrid architecture is described in, for example, U.S. patent application Ser. No. 09/549,368 to T. J. Endres et. al. entitled “A Hybrid Soft and Hard Decision Feedback Equalizer,” filed on Apr. 14, 2000, which is incorporated herein by reference.
Many receivers employ diversity combining, where different received signal streams (e.g., different multipath signals) are combined within the equalizer itself prior to generating symbol estimates. A typical diversity receiver with feedback applies different forward filters to each received signal stream and additively combines the forward filter output signals. This combined output signal is then passed through a single feedback filter, which may be either a linear feedback filter or a decision feedback filter. Systems possessing diversity combining are also known as multi-channel systems. Two well-known types of diversity are spatial and temporal diversity. Spatial diversity results from the use of multiple sensors (for example, antennas for terrestrial broadcasting). Temporal diversity results from sampling signals at rates faster than the transmitted symbol rate. Equalizers that use temporal diversity are known as fractionally spaced equalizers.
Another form of diversity is phase diversity, which arises when a real-valued data source, such as a pulse amplitude modulated (PAM) or a Vestigial Sideband (VSB) modulated source, is processed at the receiver using complex-valued filtering. An optimal minimum mean square error (MMSE) receiver for estimating the received, complex VSB signal comprises a complex-valued forward filter (i.e., a filter operating on complex signals), followed by a real-valued feedback filter (i.e., a filter operating only on the real component of the forward filter output). This type of equalizer is termed a single-axis equalizer and is described in, for example, A. Shah et al., “Global convergence of a single-axis constant modulus algorithm,” Proceedings of the Statistical Signal and Array Processing Workshop, Pocono Manor, Pa., August 2000 which is incorporated herein by reference.